Question

a car traveling at 58kmph overtake another car traveling at 40 kmph. Assuming each car is 5 m long, find the time for overtaking.​

Answer 1

Answer:

$\boxed{\sf Time \ taken \ for \ overtaking = 2 \ s}$

Given:

Speed of car 1 ($\sf v_{1}$ ) = 58 km/h

Speed of car 2 ($\sf v_{2}$ ) = 40 km/h

Length of each car = 5 m

To Find:

Time taken for overtaking car 2 by car 1

Explanation:

As we know,

$\sf 1 km/h = \frac{5}{18} \ m/s$

So,

$\sf v_{1} = 58 km/h$

$\sf =58 \times \frac{5}{18} \ m/s$

$\sf = 29 \times \frac{5}{9} \ m/s$

$\sf = \frac{145}{9} \ m/s$

$\sf v_{2} = 40 km/h$

$\sf =40 \times \frac{5}{18} \ m/s$

$\sf = 20 \times \frac{5}{9} \ m/s$

$\sf = \frac{100}{9} \ m/s$

$\sf Relative \: speed \: of \: car \: 1 \: w.r.t \: car \: 2 = v_1 - v_2$

$\sf = \frac{145}{9} - \frac{100}{9}$

$\sf = \frac{145 - 100}{9}$

$\sf = \frac{45}{9}$

$\sf = 5 \: m/s$

Total distance to be covered in overtaking = Sum of length of both the cars

= (5 + 5) m

= 10 m

$\boxed{ \bold{\sf Time \ taken = \frac{Distance \ covered}{Speed}}}$

Substituting values of Distance covered & speed in the equation:

$\sf \implies Time \: taken = \frac{10}{5}$

$\sf \implies Time \: taken = \frac{2 \times \cancel{5}}{ \cancel{5}}$

$\sf \implies Time \: taken = 2 \: s$

$\therefore$

Time taken for overtaking car 2 by car 1 = 2 seconds